Electrical – Can latching relay make the switch if the coil is powered by either of its switching circuits

I am thinking of making a set up whereby the latching relay will switch between two 9V circuits from separate power sources. However the relay coils themselves must be powered by either of the 9v running through either of the switching circuits. Thus, this may prevent the latching relay from working, but I wanted to get an opinion if this might still work. This latching relay coils are operated with 9v. The schematic of this latching relay is shown here:

The first 9v circuit will run between pin 8 and 5, and the other independent 9v circuit will run between pins 9 and 12. My question is if the coil power is powered by either of the two switching circuits, can the latching relay still operate and make the switch? To explain further, what I mean is that assuming the relay starts off in a 'set' condition, I will use the 9v power supply running from pin 8 to 5 to power both set and reset coils. When I trigger a reset condition across pins 16 and 1, most certainly the 9v power supply from the circuit across pin 8 and 5 going to the set coil (pins 16 and 1) will momentarily falter, however, my question is whether will the reset coil still be able (to be fast enough) to make the relay switch to allow the circuit across pin 9 and 12 to work, or will if not work because the reset coil does not have enough power to make the switch?

^{simulate this circuit – Schematic created using CircuitLab}

Circuitlab doesnt have the relay model I am seeking to use, however, shown here is the schematic of the cicruit I intend to use. Note that unlike the relay shown in the schematic, the configuration of my latching relay would be such that one of the 9v circuits would be connected at any time (set or reset). I have excluded the flyback diodes (which would otherwise connect from the GND to the 9v) to make the diagram less cluttered.